
Journal of Convex Analysis 27 (2020), No. 3, 811832 Copyright Heldermann Verlag 2020 Differentiability of the Argmin Function and a Minimum Principle for Semiconcave Subsolutions Julius Ross Dept. of Mathematics, Statistics and Computer Science, University of Illinois, Chicago, IL 60607, U.S.A. julius@math.uic.edu David Witt Nyström Dept. of Mathematical Sciences, University of Gothenburg, 41296 Göteborg, Sweden david.witt.nystrom@gu.se [Abstractpdf] Suppose $f(x,y) + \frac{\kappa}{2} \x\^2  \frac{\sigma}{2}\y\^2$ is convex where $\kappa\ge 0, \sigma>0$, and the argmin function $\gamma(x) = \{ \gamma : \inf_y f(x,y) = f(x,\gamma)\}$ exists and is single valued. We will prove $\gamma$ is differentiable almost everywhere. As an application we deduce a minimum principle for certain semiconcave subsolutions. Keywords: Argmin function, differentiability, minimum principle, semiconcave subsolutions. MSC: 28B20, 58C06. [ Fulltextpdf (168 KB)] for subscribers only. 